Questions
4–6 questions per board or entrance paper
Difficulty
Medium
Importance
Core — high weightage for entrance exams
Overview
Work and Energy defines the fundamental relationship between force, displacement, and the capacity to perform physical tasks in a mechanical system. Mastering this topic is essential as it forms the bedrock for advanced classical mechanics, thermodynamics, and electrical engineering problems in competitive exams.
Mechanical Work
Work is defined as the product of the component of force in the direction of displacement and the magnitude of displacement. It is a scalar quantity and can be positive, negative, or zero depending on the angle between the force and displacement vectors.
- W = Fs cos(theta)
- SI Unit: Joule (J) or N-m
- Work is zero if theta = 90 degrees
- Positive work: force and displacement are in the same direction
- Negative work: force opposes displacement, e.g., friction
Kinetic and Potential Energy
Energy is the capacity to do work, categorized primarily into kinetic energy (motion) and potential energy (position/configuration). These energies are interchangeable within a conservative field, such as gravity.
- Kinetic Energy (KE) = 1/2 mv^2
- Work-Energy Theorem: W = delta(KE)
- Gravitational Potential Energy (PE) = mgh
- Spring Potential Energy = 1/2 kx^2
- Energy is a scalar quantity
Power and Efficiency
Power measures the rate at which work is done or energy is transferred. In engineering contexts, power is often calculated as the product of force and velocity, making it a critical metric for machine output.
- P = W/t
- P = Fv (for constant force)
- 1 Horsepower (hp) = 746 Watts
- Efficiency = (Useful Power Output / Power Input) * 100
- SI Unit: Watt (W) or J/s
Conservation of Energy
The Law of Conservation of Energy states that total energy in an isolated system remains constant. It cannot be created or destroyed, only transformed from one form to another, which simplifies complex dynamics problems.
- Total Mechanical Energy (E) = KE + PE = Constant
- Applicable only when non-conservative forces like friction are ignored
- PE is relative to a chosen reference level
- Change in total energy = Work done by non-conservative forces
Formula Sheet
W = Fs cos(theta)
KE = 1/2 mv^2
PE = mgh
P = Work / Time
P = Fv
W = delta(KE) = 1/2 m(v^2 - u^2)
Total Energy E = KE + PE
Exam Tip
Always verify if the force and displacement are parallel or perpendicular before plugging values into W = Fs cos(theta), as the cosine term is the most common trap.
Common Mistakes
- Confusing the angle in the work formula by using sine instead of cosine.
- Neglecting to convert units (e.g., grams to kilograms or km/h to m/s) before applying kinetic energy formulas.
- Forgetting that negative work can be done by forces like friction or gravity acting against motion.
More Revision Notes
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